THE PRECISE AND NEW ANALYSIS FOR A MODE Ⅲ GROWING CRACK IN AN ELASTIC-PERFECTLY PLASTIC SOLID

The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material.The significance of this paper is that the usual small scale yielding theory has been broken through.By obtaining the general solutions of the stresses and the displacement rate of the near crack line plastic region,and by matching the general solutions with the precise elastic fields(not the usual elastic K-dominant fields)at the elastic-plastic boundary,the precise and new solutions of the stress and deformation fields,the size of the plastic region and the unit normal vector of the elastic-plastic boundary have been obtained near the crack line.The solutions of this paper are sufficiently precise near the crack line region because the roughly qualitative assumptions of the small scale yielding theory have not been used and no other roughly qualitative assumptions have been taken,either.The analysis of this paper shows that the assumingly'steady-state case'for stable crack growth,which has been discussed attentively in previous works,do not exist,and the plastic strains near the crack line do not have singularities,Two most important cases for stable crack growth have been discussed.

A TIME DOMAIN METHOD FOR QUASI-STATIC ANALYSIS OF VISCOELASTIC THIN PLATES

Based on the Boltzmann's superposition principles of linear viscoelastic materials and the von Karman's hypotheses of thin plates with large deflections, a mathematical model for quasi-static problems of viscoelastic thin plates was given. By the Galerkin method in spatial domain, the original integro-partial-differential system could be transformed into an integral system. The latter further was reduced to a differential system by using the new method for temporal domain presented in this paper. Numerical results show that compared with the ordinary finite difference method, the new method in this paper is simpler to operate and has some advantages, such as, no storage and quicker computational speed etc.

DEM Simulations of Resistance of Particle to Intruders during Quasistatic Penetrations

Based on the discrete element method and hydrostatics theory,an improved Archimedes principle is proposed to study the rules pertaining to resistance changes during the penetration process of an intruder into the particulate materials.The results illustrate the fact that the lateral contribution to the resistance is very small,while the tangential force of the lateral resistance originates from friction effects.Conversely,the resistance of particulate materials on the intruder mainly occurs at the bottom part of the intruding object.Correspondingly,the factors that determine the resistance of the bottom part of the intruding object and the rules pertaining to resistance changes are analyzed.It is found that when the volume density and friction coefficient of the particles and the radius of the bottom surface of the cylindrical intruder are varied,the resistance–depth curve consists of a nonlinear segment and a linear region.The intersection of the two stages occurs at the same location h/˜R=0.15±0.055.The slope of the linear stage is determined by the friction coefficient of the particles.Accordingly,the relationship between the slope and the friction coefficient is quantified.Finally,it is shown that the slope is independent of the geometry of the intruder.

Analysis of the Quasi-Static Buffeting Responses of Transmission Lines to Moving Downburst

Downburst event is identified as a major cause to failure of transmission lines in non-coastal regions.In this paper,a novel nonlinear analytical frame for quasi-static buffeting responses of hinged and multi-span insulator-line systems are derived based on the theory of cable structure.The closed-form solutions are presented and applied to predict nonlinear response including displacements and other reactions of the system subjected to a moving downburst wind in a case study.Accuracy and efficiency of the derived analytical frame are validated via comparisons with results from finite element method.

Stiffness of high-speed cylindrical roller bearing subjected to radial force and bending moment

Presents a practical way of calculation for stiffness of cylindrical roller bearing based on traditional quasistatic analytical methods subject to radial force and bending moment,which take into consideration the effect of such factors as thickness of oil elastohydrodynamic film,pressure,shear force,friction force of cage,centrifugal force and slides,taken into consideration and presents the results of stiffness calculation with a typical example with an aeroengine cylindrical roller bearing were given in the paper.And,discusses the effect of major parameters’influence on stiffness.

Quasistatic magnetic fields generated by a nonrelativistic intense laser pulse in uniform underdense plasma

Quasistatic magnetic fields generated by nonrelativistic intense linearly polarized （LP） and circularly polarized （CP） laser pulses in an initially uniform underdense plasma in the collision-dominated limit are investigated analytically. Using a selfconsistent analytical model, we perform a detailed derivation of quasistatic magnetic fields in the laser pulse envelope in the collision-dominated limit to obtain exact analytical expressions for magnetic fields and discuss the dependence of magnetic fields on laser and plasma parameters. Equations for quasistatic magnetic fields including both axial componentBz and the azimuthal one Be are derived simultaneously from such a selfconsistent model. The dependence of quasistatic magnetic field on incident laser intensity, transverse focused radius of laser pulse, electron density and electron temperature is discussed.

Nonlinear deformation of a cantilever incompressible poroelastic beam under a uniform load

Nonlinear bending of cantilever incompressible poroelastic beams subjected to a uniform load is investigated with the constraint that fluid flow is only in the axial direction. The governing equations for large deflection of the poroelastic beam are derived from theory of incompressible saturated porous media. Then, nonlinear responses of a cantilever beam with impermeable fixed end and permeable free end are examined with the Galerkin truncation method. The deflections and bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressures are shown in figures. The differences of the results between the large deflection and the small deflection theories are analyzed. It is shown that the results of the large deflection theory are smaller than those of the small deflection theory, and the time needed to approach their stationary states for the large deflection theory is shorter than that for the small deflection theory.

Review of the experimental studies of the cracking behaviors of fracturedrocks under compression

In recent years, many useful experimental results on the cracking behaviors of fractured rocks have been obtainedvia uniaxial, biaxial, triaxial, and Split Hopkinson Pressure Bar (SHPB) tests. In this paper, the influence of theinclination angle of flaws, number of flaws, and patterns of cracks on the mechanical properties during the failureprocess under static loading and dynamic loading conditions is introduced and reviewed. The results show thatthe presence of cracks can decrease the strengths of precracked specimens, and the inclination angles, numbers,and crack patterns of pre-existing flaws can change the mechanical properties and cracking behaviors of precracked specimens. Under static loading, the closer the inclination angle is to 90, the greater the strength, theelastic modulus, and the peak strain of the precracked specimen. However, under dynamic loading, the influenceof the inclination angle varies, and the strength can increase or decrease, possibly in a V-shaped manner. Thischange can be determined by multiple factors, such as the loading path, the materials of the precracked specimen,and the number of pre-existing cracks. Under dynamic loading, the precracked specimen usually exhibits an Xshaped conjugated failure. Additionally, some problems in the study of the cracking behaviors of fractured rocksand related future research are described and presented, and corresponding suggestions and solutions are given.In particular, excavation in deep rock engineering, support of the rock surrounding the tunnel, and mining engineering have important scientific and engineering significance.

Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model

This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.

Homogenization with the Quasistatic Tresca Friction Law:Qualitative and Quantitative Results

Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law,and studies the homogenization theories under the frameworks of H-convergence and small ε-periodicity.The qualitative result is based on H-convergence,which shows the original oscillating solutions will converge weakly to the homogenized solution,while the author’s quantitative result provides an estimate of asymptotic errors in H^(1)-norm for the periodic homogenization.This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.

Experimental studies of axial magnetic fields generated in ultrashort-pulse laser-plasma interaction

The quasistatic axial magnetic fields in plasmas produced by ultrashort laser pulses were measured by measuring the Faraday rotation angle of the backscattered emission. The spatial distribution of the axial magnetic field was obtained with a peak value as high as 170 Tesla. Theory suggests that the axial magnetic field is generated by dynamo effect in laser-plasma interaction.

Geometry independent C^(*)-T_(z) dominance of three-dimensional quasistatic growing crack-tip fields in creeping solids

In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo into three-dimensional solution(3D)for stationary cracks under the domination of C^(*)with the constraint factor Tz.However,how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging.In this study,we reveal that,for 3D quasistatic growing cracks,the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8%for relative creep time up to 0.8 in various specimens with finite thickness.For a given relative time,Tz distributions can be unified by the equivalent thickness concept,Beq.The results show that C^(*)-T_(z) can effectively quantify both the load and constraint effects on the crack-tip fields.Such geometry independent dominance can considerably simplify the treatments of load and constraint effects,thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.